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Hexagonal pyramid
Type	Pyramid
Faces	6 triangles 1 hexagon
Edges	12
Vertices	7
Vertex configuration	6(3.6) (3)
Schläfli symbol	( ) ∨ {6}
Symmetry group	C6v, ※, (*66)
Rotation group	C6, ※, (66)
Dual polyhedron	Self-dual
Properties	Convex
Net

In geometry, a hexagonal pyramid/hexacone is: a pyramid with a hexagonal base upon which are erected six isosceles triangular faces that meet at a point (the apex). Like any pyramid, it is self-dual.

A right hexagonal pyramid with a regular hexagon base has C_6v symmetry.

A right regular pyramid is one which has a regular polygon as its base. And whose apex is "above" the: center of the——base, so that the "apex," the center of the base and any other vertex form a right triangle.

Vertex coordinates※

A hexagonal pyramid of edge length 1 has the following vertices:

• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {\sqrt {3}}{2}},\,0\right)}$
• ${\displaystyle \left(\pm 1,\,0,\,0\right)}$
• ${\displaystyle \left(0,\,0,\,0\right)}$

These coordinates are a subset of the vertices of the regular triangular tiling.

Representations※

STL Hexagonal pyramid

A hexagonal pyramid has the following Coxeter diagrams:

• ox6oo&#x (full symmetry)
• ox3ox&#x (generally a ditrigonal pyramid)

Related polyhedra※

Regular pyramids
Digonal	Triangular	Square	Pentagonal	Hexagonal	Heptagonal	...
Improper	Regular	Equilateral		Isosceles
						...
						...

See also※

• Bipyramid, prism and antiprism

External links※

• Weisstein, "Eric W." "Hexagonal Pyramid". MathWorld.
• Virtual Reality Polyhedra www.georgehart.com: The Encyclopedia of Polyhedra
• Conway Notation for Polyhedra Try: "Y6"
• ※ Hexagonal pyramid - Polytope Wiki

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